Solutions - Categorical Variables11.3 FBI statistics: a) These distributions refer to those of x at given categories of y. RACE OF VICTIM RACE OF MURDERER Blacks Whites Blacks 91% 17% Whites 9% 83%b) x and y are dependent because the probability of a murderer being of a certain race changes greatly according to the race of the person murdered.11.9 Happiness and gender: 1) The assumptions are that there are two categorical variables (gender and happiness in this case), that randomization was used to obtain the data, and that the expected count was at least five in all cells. 2) :0HGender and happiness are independent. :aHGender and happiness are dependent. 3) (2980.022=-=∑CountExpectedCountExpectedCountObservedχ4) P-value: 0.87 5) The P-value is quite large. If the null hypothesis were true, the probability would be 0.67 of getting a test statistic at least as extreme as the value observed. It is plausible that the null hypothesis is true, and that gender and happiness are independent. With a significance level of 0.05, we could not reject the null hypothesis.

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